To download a file, click on the desired format - "mp3", "wma", "mov", etc.
If you see an arrow button, clicking on it will play the track in Flash form, which is faster than downloading and doesn't use any disk space on your machine. The playback may take a few seconds to begin, after which the arrow turns to a "Pause" symbol. Clicking on the "Pause" button will stop playback.
If you don't see an arrow button, you may want to install Flash (it's free), which can be found here. Some mobile devices don't support Flash.
If there's an "Amazon" link for the track, it will take you to Amazon.com where you'll be able to audition and buy it.
If there's an "iTunes" link for the track, then clicking that will take you to the iTunes Music Store where tracks can be auditioned and purchased. If you don't have the iTunes application on your computer you have to download that (it's free) before you can use the store. The iTunes application can be found here.
Other free media tools you may want are Quicktime (for .mp3, .mov and other formats) or Windows Media Player (for .wma and others).